Which is the best for burning fat, strength training or cardio? The best answer is both, but there is a bit more to it. You're going to burn a lot more fat if you're strength training and pumping your heart on a regular basis.
But, for those of you who really must know, weight lifting will give you more fat-burning power for your efforts. Here's the long answer: cardio tends to burn more calories while you're doing it. That's why you tend to get hot and sweaty during your morning run. Cardio also has a fat-burning effect that lingers for 3-4 hours after you're done. Strength training, on the other hand, burns fat for 3-4 days! That's because when you weightlift, you cause microscopic damage to your muscles. The muscles spend the next few days repairing that damage- and using fat as the fuel to do so!
Intensity also matters. The higher the intensity of your workout, the more tissue damage. This means your body will work that much more over the next several days to repair the damage done.
One last tip: it's best not to do your cardio right before your weight lift. Your body needs energy and fuel in order to get a good strength training workout.
A well designed strength training plan focusing on your large muscle groups will actually help to turn your body into a fat burning machine. Don't waste time on smaller muscle groups though like biceps and triceps. Those will take care of themselves. Work the large muscles of your legs, upper back and chest to get the most bang for your buck!